In this paper, we give a method which allows us to construct a class of Parseval frames for L2(R) from Fourier frame for L2(I). The result shows that the function which generates a Gabor frame by translations and modulations has "good" properties, i.e., it is sufficiently smooth and compactly supported.
A sufficient condition for affine frame with an arbitrary matrix dilation is pre- sented. It is based on the univariate case by Shi, and generalizes the univariate results of Shi, Casazza and Christensen from one dimension with an arbitrary real number a (a > 1) dilation to higher dimension with an arbitrary expansive matrix dilation.
